On familysearch there is a Baptism for a Thomasina Lockhart, parents Alexander and Margaret, 14 Jan 1897, but on my phone so it doesn't show me all details - just Northumberland.
I assume you don't have his marriage certificate with father's name?
There is an entry on there too for Chelsea Pension record for an Alexander Lockhart, born 1873, Northumberland. I'm sure someone can look into that for you (sorry can't at the moment!).
Also on FreeBMD, birth of Alexander Lockhart, Dec qtr 1873, Newcastle T, 10b 59.Maybe?? Or have you looked into that one?